3 years ago

Theoretical bounds for the exponent in the empirical power-law advance-time curve for surface flow.

Allen G. Hunt, Hamed Ebrahimian, Behzad Ghanbarian, M. Th. van Genuchten

A fundamental and widely applied concept used to study surface flow processes is the advance-time curve characterized by an empirical power law with an exponent r and a numerical prefactor p (i.e., x = p*t^r). In the literature, different values of r have been reported for various situations and types of surface irrigation. Invoking concepts from percolation theory, we related the exponent r to the backbone fractal dimension Db, whose value depends on two factors: dimensionality of the system (e.g., two or three dimensions) and percolation class (e.g., random or invasion percolation with/without trapping). We showed that the theoretical bounds of Db are in well agreement with experimental ranges of r reported in the literature for two furrow and border irrigation systems. We also used the value of Db from the optimal path class of percolation theory to estimate the advance-time curves of four furrows and seven irrigation cycles. Excellent agreement was obtained between the estimated and observed curves.

Publisher URL: http://arxiv.org/abs/1801.09182

DOI: arXiv:1801.09182v1

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